rec-erc-72-4 - usbr.gov 'porous materials1 water measurement1 infiltration ratel permeability...
TRANSCRIPT
Eugene R. Zeigler & . Engineering and Research Center
Bureau of Reclamation
January 1972
Januarv 1972 Laboratory Tests to Study Drainage from 6. PERFORMING ORGANIZATION CODE
Sloping Land
I 8. PERFORMING ORGANIZATION
REPORT NO.
Eugene R. Zeigler RECERC-72-4
9. PERFORMING ORGANIZATION NAME A N D ADORES5 10. WORK UNIT YO.
~ngineering and Research Center '' 11. CONTRACT OR GRANT NO.
Bureau of Reclamation Denver, Colorado 80225 ,I. !.
I 13. TYPE OF..REPORT LND PERIOD COVERED .=.;--- --
2 . SPONSORING AGENCY NAME A H 0 ADDRESS
r, ~.,.! .. , ~ -. >. ,,'~. ,.-
Same ..L...,~
, .~ . 14. SPONSORING AGENCY CODE '' . - ~ ...
., ., I 5 . SUPPLEMENTARY NOTES
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6. ABSTRACT
An investigation was made to study drainage from sloping land. A tilting sand tank (flow tank) 2 ft wide, 2-112 ft deep, and 60 ft long was used. Drains to simulate agricultural tile were placed in the sand tank at 6-ft intervals 2 ft above the tank bottom. Water (recharge) was applied at a steady rate on the sand surface to simulate irrigation. Drain discharges and water table profiles were measured for 54 tests with different recharge rates, 6- and 12-ft drain spacings, and sand tank slopes from 0 t o 10%. Four tests were made introducing dye into the tank and streak-lines obtained showing directions of water movement in the sand. Pressure measurements were made at points on the tank side to obtain the ~otential field between drains. An equilibrium area occurred in the middle length of the sloping sand tank where the drain dixharges equaled the amount of water applied between two operating drains. This condition occurred during all tests, regardles of slope, recharge rate, or drain spacing. For a given recharge rate and in the equilibrium area, water table profiles measured perpendicular to the tank bottom were the same for slopes between 0 to 10%. The report includes tables of the drain discharges, plots of the water table profiles, photographs of the dye streak-lines, and diagrams showing the potential field occurring between drains. Effects of slope and recharge rate upon drain dixharges, water table profiles, and water movement in the sand tank were analyzed.
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7 . KEY WORDS AND DOCUMENT ANALYSIS '.'
a. DESCRIPTORS- /groundwater flow1 subsurface drains1 water table1 steady flow1 horizontal drains1 'subsurface drainagelilaboratory testsl 'test results1 plastic tubing1 slopes1 water recirculation1 *groundwater movement1 'porous materials1 water measurement1 infiltration ratel permeability testsl effects
5. IDENTIFIERS--
!vailrrble from the National Technical Information Service. Operations Xvision, Sprlngfleld. Virginia 22151.
DRAINAGE FROM SLOPING LAND
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2..
by .. .
Eugene R.-Zeigler
January 1972 -
Hydraulics Branch Division of General Research Engineerin and Research Center 7 Denver, Co orado
UNITED STATES DEPARTMENT OF THE INTERIOR * BUREAU OF RECLAMATION Rogers C. B. Morton < Ellis L. Armstrong Secretary Commissioner
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. . . . . . . . . . . . . . . . . . . .
I . Water Recirculating System . 7 . 1 Wells and Manometers for Mfiasuring the Water j!
Table Location . . . . . . . . . . . . . . . . . . . . . . . . . ! . . .. 4 ;/
.;, ., ., The Testing Program and ~ k s t Procedures . . . . . . . . . . . . . . . . . " . .
+ 9' ' (i
- , . . . . . . . . . . . . . . . . . . . . . . . . . . . Types of Tests 4 Phase 1. Tests far Measuring Drain Discharge
4 . . . . . . . . . . . . . . . . . . . . . and Water Table Locations Phase 2, StreakGne Tests Investigating Direction ..
. . . . . . . . . . . . . . . . . of Water Movement Through the Sand : 5 Phase 3, Pressure Measurement Tests . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . : . . 5 ,: Phase 4, Sand Tank Permeability Tests ;. : 6 I
. . . . . . . . . . . . . . . . . . . . . . Results of the Test Program 6
Drain Discharge and Water Table Tests . . . . . . . . . . . . . . . . . . . 6 Streak-Line Tests lnvestigating Direction of Water
Movement Through the Sand . . . . . . . . . . . . . . . . . . . . . 7 Pressure Measurement Test:, .:i . . . . . . . . . . . . . . . . . . .
, , ./ 7
Discussion and Analysis of Test Results . . . . . . . . . . . . . . . . . . 7
Zero Percent Slope Tests . . . . . . . . . . . . . . . . . . . . . . . 7 Equilibrium in the Sand Tank . . . . . . . . . . . . . . . . . . . . . 8 Effect of Slope and Recharge Rate Upon the
Water Table Profile . . . . . . . . . . . . . . . . . . . . . . . 9 9 . . . . . . . . . . . Effect of Slope and Recharge Rate Upon Drain Discharge
Streak-Lines and Direction of Water Movement Through the Sand Tank . . . . . . . . . . . . . . . . . . . . . . . . . 10
Pressure Measurement Tests . . . . . . . . . . . . . . . . . . . . . 11 Influence of the End Drain Envelopes . . . . . . . . . . . . . . . . . 11 Flow of Water Downslope Passing Beneath the Drains . . . . . . . . . . . . 12 Development of Water Movement Reneath Drains . . . . . . . . . . . . . 13 Location of the First Upslope Drain . . . . . . . . . . . . . . . . . . 14
LIST OF FIGURES
+: Figure - , t i
1 Ground-water drain details . . . . . . . . . . . . . . . . . . 22 2 Water circulating sfstem for the sand tank . . . . . . . . . . . . . 23
Calibration curve recharge Uriit No. 10 . . . . . . . . . . . . . . 24 Ground-water table measuring wells . . . . . . .: . . . . . . . . 25 a. Water table profiles normal to the bottom of
the sand Tank . . . . . . . . . . . . . . . . . . . . . 26 b. Trigonometric computations made to mrrect manometer
readings . . . . . . . . . . . . . . . . . . . . . . . 26 Water table profiles-0 percent slope . ., . . . . . . . . . . . . . 27 Water table profiles-7-1/2 percent slope, 6-foot
drain spacing . . . . . . . . . . . . . . . .~ . . . . . : 29 Streak-line tests showing formation of streamlines . . . . . . . . . . 31 Streak-line tests showing the flow system of the recharge'
flowing into the drains . . . . . . . . . . . . . . . . . . . 32 Strealelhe tests showing the f!?w cystem of water -:: : . .
passing bnneath the drains . - . . . . . . . . . . . . . . . . . 34 Streak-line tests showing iecharge flowing beneath i:
the drain . .~ . . . . .. . . . . . . . . . . . . . . . . : . 35 Streak-line tests showing stre'imlines entering the ::.
end drain envelope . . . . . . . . . . . . . . . . . . . . 36 Pressure measurements . . . . . . . . . . . . . . . . . . . . 37 Equal potential and flow lines determined from
pressure measurements . . . . . . . . . . . . . . . . . . . 39 !',
Equal potential and flow lines determined from pressure measurements . . . . . . . . . . . . . . . . . . . .40
Equal potential and flow lines determined from pressure measurements . . . . . . . ': . . . . . . . . . . . 41
Equal potential and flow lines determined from pressure measurements . . . . . . . . . . . . . . . . . . . 42
Recharge rate-Water table elevations midway between the drains at 0 percent slope . . . . . . . . . . . . . . . . . 43
Comparison of measured water table profiles with water table profiles computed by using Dupuit-Forchheimer assumptions, 0 percent slape tests . . . . . . . . . . . . . . . 44
Water table profiles between Drains No. 6 and 8 .-. by slope . . . . . . . . . . . . . . . . . . . . . . . - ; 45
Water table profiles between Drains No. 6 and 8 by recharge rate . . . . . . . . . . . . . . . . . . . . . . 46
Water table profiles normal to the tank bottom-6-foot . . drain spacing . . . . . . . . . , . . . . . . . . . . . . &
Water table profiles normal to the tank bottom-6-foot drain spacing . . . . . . . . . . . . . : . . . . . . . . 49
Water table profiles normal to the tank bottom-12-foot drain spacing . . . . . . . . . . . . . . . . . . . . . . 51
Water table profiles normal to the tank bottom, 12-foot drain spacing . . . . . . . . . . . . . . . . . . . 53
Diagram showing streamlines of flow entering an end .. ~. . .
drain envelope . . . . . . . . . . . . . . ;. . . . . . 55 Diagram showing method for controlling height of water,?
table profile near endllrain No. 11 . . . . . : . . . . . . . . 55 Water table profiles between Drains No. 8, 10, and 11
by recharge rate . . . . . . . . . . . . . . . . . . . . . 56 Example of input-Output analysis to determine flow
downslope passing beneath the drains . . . . . . . . . . . . . . 57 Downslope flow passing bsneath the drains . . . . . . . . . . . . . 58
Table
Streamlines of f low for a constant recharge rate and varying slope . . . . . . . . . . . . . .
Streamlines of f low for a constant slope and varying recharge rate . . . . . . . . . . . . . .
Location of the perpendicular 2-foot elevation for the water table at the upsiope end o f the sand tank .
LIST OF TABLES
Locations o f the ground-water table meazurlng wells . Summary of test performed . . . . . . . . . . D l a ~ n discharges . . . . . . . . . . . . . . Flow in rnl/sec downslope passmg beneath the drams .
The Bureau of Reclamation plans, designs, and of the tank was constructed from transparent plastic constructs many irrigation projects in the Western panels. United States. On most projects the addition of irrigation water raises the ground.water table, Water was placed in the tank before filling the tank sometimes to damaging heights. Subsurface agricultural with sand. Sand was placed in the water and mixed drains are usually required t o control tho ground water with a. shovel to prevent air bubbles being trapped in and also to prevent unfavorable salt balances from the voids between individual sand grains. Themean occurring within the plant root zone. In recent years sand diameter was 0.2 millimeter (mm). The depth o f there has been ar: increased use of sprinkling systems sand in the tank was approximately 2 feet 5 inches for irrigating. These sprinkling systems can irrigate land (0.74 m). ; having steeper slopes than the older furrowtype ,/ method o f irrigation. Thus, a more frequent use of . ,Drain Construction and Location,,-. drainage systems on sloping land is anticipated. The ,l!
Eleven hociiontal drains, to simulate ag~.icultural drains, w<e placed perpendicular to the sides of sand tank.. One end of the drain butted against the'. . : transparent side of the tank and the drain passed .. through the other side o f the tank. The drain effluent dumped into a collection trough. Drains were spaced at 6-ft (1.83.m) intervals along the 60-f: (18.29-m) length of the tank. The centerline of the drains was 2 f t (0.61 m l above the tank bottom. Location and numbering of the drains are shown on Figure 1.
purpose o f this investigation was to obtain basic knowledge about the f;ow in porous media' for agricultural drains on sloping land. The emphasis of the investigation was directed toward determining what effect various slopes and recharge rates have upon the location of the water table, upon drain discharges, and path of water flow through the soil, Because of the basic nature of the study no attempt was made to determine design parameters for placement of .&ins.
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THE TEST APPARATUS :, '; ,., ,
Generai ,I
A t e s t facility was designed to simulate steidy state flow conditions of agricultural (interceptoll) drains operating on sloping land. The test facility / , i s a very simplified representation of a hillside with ag'ricultural tile drains. None of the complex or vario~is aquifer formations that may:exist on hillsides was sinrulated in the test facility. his tacility consisted o f a ryand tank having drains spaced at regular intervals. VVater was applied at'?; steady rate upon the sand suiface. The water after dropping upon the sand surface flowed into the water table, through the sand into the drains, and finally flowed out of the drains.
I Sand Tank
The photogrsphs on page 2 show each side of the sand tank.
The sand tank rested on two large beams. The beams. which were longitudinal t o the sand i!ank, were supported at two points. One support was a pivot point and the second support a lifting point. Two chain hoists were used to l i f t the sand tank. Thecslope of the sand tank could be varied betweer;O and 12 percent. The sand tank was 60 feet (ft) (18.29 mete:&)) long, 2.112 f t (0.76 rn) deep. and 2 f t (0.61 m) wide (inside
The drains were constructed from plastic tubing with an outside diameter o f 518 inch '(1.59 centimeters (cm)) and all inside diameter of 112 inch (1.27 cm). On one side of the tube lI l6. inch (0.16-cml wide slots were cut perpendicularly in the tube and spacad at 1-inch (2.54-cml intervals along the tube. The slots extended about halfway' through the tube. On the other side o f the tube the slots were offset 112 inch (1.27 cm) from the opposite slots. To prevent the fine sand>,base material from entering the drain, an envelope of Nb. 16 sand was placed around the drain. The envelope was 0.2 f t (6.1 cm) outside diameter. The photographs on page 3 show the sequence of placing a ground-water~drain in the sand tank.
The drain at each end o f the sand tank had the No. 16 sand envelope; extending from the bottom of the tylnk to the top o f the sand surface, Figure l-Detail 0. l'he end drain enbelope was 0.5 f t (15 cm) thick. The purpose of thkse envelopes was t o provide versatility for making reits. I f needed, additional water could be added or withdrawn from the envelopes. Also, the water table elevation within the envelope could be controlled. This type envelope was helpful in making permeability tests.
Water Recirculating System
The water rectrculating system conslsted of a set of recharge units, the drains, a collection trough, and a
collection tank, Figure 2. The purpose of the water recirculating system, was to keep y z a r flowing through the sand tank at r@:.;&mperature. The dissolved air in the water woilld be at equilibrium with thc temperature and pressure of air around the sand rank. This prevented the tendency for air to come out of solution and collect in voids between the sand grains, and thus change the permeability of sand in the tank. Previous experience showed that cold water from the high-pressure water supply system had an abundance of dissolved air.
There wcre 10 recharqe units (Figure 28) on top of the sand tank. Each recharge unit consisted o i two plastir wbes that applied water to the sand surface, an orifice to measure the applied water, and a differential manometer. The plastic tubes were positioned'between the drains. The plastic tubes of the recharge units were placed with the discharge holes (diameter 0.020 inch (0.51 mm)) pointing up to prevent clogging. With the aid of rubber bands small plastic caps were held over the holes. The caps caught the small jets squirting from the tbbes and changed the jets into drops of water falling directly beneath the caps The recharge tubes were maintained in a horizontal position for the'^ various sand tank slopes so different vertical distances did not occur between discharge holes on the same tube. This procedure made the recharge application rate uniform over-:hs entire area.
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The discharge from each; recharge unit [Figure 2C) was mepsured with a small orifice plate whose diameter was 0.078 inch 11.98 cml. Preliminary testing showed slight variatiuns of the differential head occurring across the 10 orifices for 1 specific discharge. Therefore, each recharge unit measuring system was calibrated separately. A calibration curve or graph was obtained (Figure 3) for each recharge unit..The points on the graph were the differential head occurring across the orifice when making a discharge measurement.;,.The discharge was measured volumetrically using a stop watch and graduated cylinder. Since the graduated cylinder was marked in milliliters, the discharge was
r-also given in mllsec.
Wells and Manometers for Measuring the Water Table Location
Plastic tubes (vertically positioned) were inserted in the top'portion of the sand tank. The plastic tube provided a well in which the water could collect. The water surface elevation within the well corresponded to the ground-water table elevation of the sand surrounding the well. Well tubes. Figure 4, were placed at approximately 1-ft (0.30-m) intervals along the sand tank. The locationof the well tubes in the sand tank i s given in Table 1.
The wells were made of 7 - l l l i nch (19.05.cm) lengt!?~~ of plastic tubing. The outside diameter of the well was 518 inch (1.59 cm) and the inside diameter was' l i2 inch (1.27 cm). The well bottom was plugged wi.?h a plastic insert. Four slots were cut in the lower poition of the well tube to allow water from the sand tank to flow into the tube. A fine No. Zr@?esh screen (Figure 48) was placed in the well tube'to prevent fine sand from entering the well tube. A copper tube and flexible tubing conveyed the pressure or water level within the well to the manometer (Figure 4A). Numbering of the manometers corre~ponded to numbering of the ground-water table measuring wells given in Table 1.
The accuracy of msasuring the vertical locat'ln of tne ground-water table was subject to the inherent measuring capabilities of glass-tubed manometers. The inside diameter of the glass tubes was approximately 6 mm. Capillary rise within the individual tubes varied .,
depending upon variation of the inside tube diameter and also upon the glass surface wnditionwithin the tube. The capillary rise was probably less than 0.02 f t (0.61 mrn). The manometer boards were marked in feet and hundredths. Manometer readir;;ls were made in thousandths of a foot by interpolation. The thZusandth foot readings were useful in determining when the water table profile was at a stable location for the steady::'tate tests.
' . , . .
THE TESTING PROGRAM AND TEST PROCEDURES
Types of Tests
The testing was done in four phases. In thef i i i t phase drain discharges were measored and the water table was detrhined between drains for various recharge rates and slopes. Tests investigating location of streamlines and path of water movement through the sand were made in the second phase. The third phase tests ccnristed of pressure measurements made through the transparent side of the sand tank, and in the fourth phase permeabi:ity tests of the aquifer sand were made in the sand tank.
Phase 1, Tests for Measuring Drain Discharge and Water Table Locations
Fifty-four different tests were made with vzrious sand tank slopes, recharge rates, and drain spacings. The sand tank slope,was varied from 0 to 10 percent, the recharge rates from 2-112 to 10 mllsec. Tests were made with 6.ft (1.83.m) and 12-ft (3.66-n) drain spacings. A summary of the tests performed are listed in Table 2. The general procedure for making a given test was as follows. Water was applied. on the sand
surface st a constant rate using the 10 recharge units., was to make the controlled water table profile the Rechargz rates were, given in milliliters-per-second same as the 0 percent profile for a given recharge rate., per-recharge unit. Forexample, a test designated with a Both water table profiles (controlled and 0 percent 2.112.mllsec recharge rate means 2-112 mllsec of water slope) would be at the $awe relative perpendicu!ar flowed from one recharge unit. The recharge rate, as location above the sand tank ilcttom. Computed values defined in the repor?, i s the discharge rate from one for manometer readings between Drains No. 10 and 11 recharge unit, and rhis discharge placed on a 12-sq f t ' were obtained"by using the 0 percent slope profile (1.1-m21 sand sur:ace area per unit time. Ac t~a l data. These computed values were obtained for each infiltration rates for the designated recharge rates slope and recharge rate. tested are listed in the following table.
Figure 26B helps show how height of the water table w t i o n rate was controlled. A flexible tube connected the end of
Designated tes t & & h e & Drain No. 11 to a small box with an overflow weir. By recharge rate ft2.sec ft2-day, m2-day raising or lowering the overflowweir, the water table
mllsec lo-s profile near the sand tank end could be raised or "owered. Elevation of the weir box was adjusted until
10 2.94 2.54 775 ., manometer readings' between Drains No. 10 and 11 7-112 2.21 1.91 581' were approximately within 0.01 f t (3 mml of the 5 1.47 1.27 388 . precomputed values.
. 4 1.18 1.02 310 3 0.98 0.85 258 Phase 2, qreak-Line Tests Investigating 2.112 0.74 0.64 194 Direction of Water Movement Through the Sand
Observaticns were madc'to determine when the sand tank roached a steady state condition. I t was found that a 4-hour time period was adequate to obtain steady state flowconditions. Drain discharges and water table data were taken only after the sand tank had reached a steady state condition.JJrain discharges were measured with a graduated cylinder and stop watch. Each set of water table data consisted of 60 manometer readings.
. For the 12-ft (3.56-rn) drain spacing tests, odd numbered Drains No. 1 through 11 were plugged for the 0 percent slope tests. For the sloping tests, end Drain No. 11 \tl;z,:unplugged to prevent water from ponding at the dovmslope end and overflowing the top of the sand tank: The end drai,n envelope was believed to influence drainage conditions up slope from the envs!ope, but how far up slope this iniluence extended
;: was unknown. Therefore, to determine the extent of this influence, two types of tests were made at each percent slope and recharge rate of the 12-ft (3.66-ml drain spacing tests.
(1) Free flow tests where discharge from Drain No. 11 was allowed to flow freely. Atmospheric pressure acted at the end drain.
(2) Controlled tests where a pressure was applied at the end of Drain No. 11.
For locating the controlled water table profiles between Drains No. 10 and 11 the standard used was the 0 percent slope water table profiles. The objective
Colored blue water was injected into the sand along the transparent side of the sand tank. "Patent 8lue"dye in a powder form was used t o color.;the water. The properties of the colored water were verygood, in that: (1) the colored water was stable in nature and the blue color did not disperse too rapidly, (2) when injected into the sand tank the colored water did not appear to have undesirable density effects, and (3) a large proportion of the colored water could be flushed from the tank without excessively staining the sand. The
,,colored water was inserted into thp sand tank at desired points through sma!l glass tubes pushed into the sand. Care was taken to insure that the tube ends were against the transparent sides of the sand tank. Colored water was intioduced into the tubes at a rate of approximately 1 to 5 drops every 5 minutes. A blue dye streak-line was formed from the tube end as the flowing v~afer moved the dye away. (The term "streak-line" instead of "streamline" is used for describing the dye tests because it is more accurate and is more descriptive of the dye tests than the term streamline.) Photographs of the streak-lines gave a vivid picture.of the ground-water movement, Figure 8. The grid on the transparent sand tank side was 3 by 3 "
inches (7.6 x 7.6 cm). Four dye streak-line tests were made with a sand tank slope of 2-112 percent. The drain spacing was 6 f t (1.83 m) and the recharge rates were 2-112.'5, 7.112, and 10 ml/sec.
Phase 3, Pressure Measurement Tens
The purpose of the pressure measurement tests was to measure or define the potent~al f~eld occurring between
drains. Pressure measurements were made through the transparent side of the tank.
Approximately 200 small holes were drilled through the transparent side of the sand tank. The holes were small enough to prevent siqd from passing through. Plastic piezometer taps were fastened to the sides and flex~ble tubes conveyed the fluid pressure to the measuring equipment. The locat~on of the piezometer taps i s shown in Figures 13A and 138. A differential pressure transducer, arrplifer, and digital readout Instrument were used in making the pressure rneasurements. The differential pressure measurements were made in feet of water and the digital readout showed the measurement in feet and thousandths. The pressure measurement was the pressure difference between an established datum'and the given piezometer tap, Figure 13C. The datum of reference was the centerline elevation of Drain No. 6. With the M o manifolds, a se~ies of 60 pressure rneasurements could be made before changing the flexible tubes to another set of 60 piezometer taps.
Twelve pressure measurement tests were made. The tests were for 0 percent slope at the 5 and 10-mllsec recharge rates, 2-11 -percent slope at the 2-112.. 5.. 7-112.. and 10-mllsec recharge rates, and for 5. 7-112, and 10 percent slopes at 2-112- and 10-mllsec recharge rates.
Phase 4, Sand Tank Permeability Tern
For ground-water studies it is important to know the permeability of the porous material. Therefore. permeability tests were made with the sand tank at a 10 percent slope. The permeability measurement represents the average horizontal permeability of the sand within the tank. The method for making the inplace permeability measurement was as follows:
The depth of water flowing within the sand tank is wntrolled at the upper and lower ends of the tank. Then the discharge and areapf water flow through the sand tank is measured. The coefficient of permeability i s computed using the following formulas:
where,
Q =discharge flowing through the sand - tank, ft3/sec
i =slope or hydraulic gradient, ftlh k = coefficient of permeability, f t l se~ A =area of flow for the given Q, ft2 y =depth of flow, f t w = 2-foot width of sand tank, i t
A small box with an overflow weir was connected to each end drain of the sand tank. Flexible tubeswere used to connect the boxes to the end drains. Al l , other drains (No. 2 through 10) were plugged. Water wes supplied to the up slope box. The water flowed with a irniform depth down the rlope through the sand tank and came out the downslope box and through the overflow weir. By adjusting elevations of the weirs, the water flow dzpth within the sand tank was established at approximately 2.3 ft (0.7 m), as measured perpendicular to the tank bottom. Water flow in the finesand was also parallel to the tank bottom near the tank ends because of the end drain envelope construction. An excessive amount of water was supplied to the up slope box so water flowed through the overflow weir. The quantity of water supplied to the up slope box and the quantity of water flowing through both overflow weirs were measured. Water depth flow through the sand tank was obtained at eaih of the 59 ground-water table measuring walls that were in the fine sand. The average depth was used to get the area of flow.
Results of the permeability tests were:
Fabruary 12, 1968 k = 0.000589 ftlsec. 50.1 fthay, (0.000177 mlsec)
December 19, 1968 k = 0.000552 ft!sec, 47.7 ftldav. (0.000168 mlsec)
Average k = 0.000566 ftlsec. 48.9 >, ftldav? (0.000172 mlsec)
RESULTS OF THE TEST PROGRAM
Drain Discharge and Water Table Tests
Q=iKA ' A = yw (1) The measured drain discharges for the tests are listed in Table 3. Also listed in Table 3 are the drain discharges
or (Percent Recharge) expressed as a percent of the . (1
recharge rate. These "drain discharge percents" were
k =& helpful in fol10,wing trends of drain discharge for the
IYW various tests.
6
Water-table elevations were determined from the manometer readings. The manometer readings were corrected for the sand tank slope and the physical location properties of the individual gro~nd-water measuring wells. An illustration of the location property and slope corrections made to the manometer readings is shown in Figures 5A and 50. A digital computer was used to make the numerous computations.
Some of the water-table profile: shown in this report were made with an X-Y plotter. Figure 6 was a graph of the water-table profiles for the 0 percent slope tests. The water-table profiles were a series of straight lines drawn from point to point. These points were the elevations of thr water table as determined at the ground-water table measuring wells. The water table profile curves are discontinuous. Breaks in the curves are made near the drains. Encircled numbers designate drain numbers as shown in Figure 1. Drain discharges and drain discharge percents are also shown on Figure 6. The drain discharge percentis the drain discharge expressed as a percent of th8 discharge rate from one recharge unit.
One graph giving water.table profiles in sloping form and for the complete tank length i s shown on Figure 7. It gives a plot of the water-table profiles for the 6-ft (1.83-m) drain spacing and 7.112 percent slope tests. The water-table profiles are divided into two sets of CuNes. Thz upper set shows the first 30 f t (9.1 m) and the lower set the last 3 0 f t (9.1 rn). In the upper set the ahissa scale i s a t the top of the figure and ordinate scale at the upper right side. For the lower set the abscissa scale i s shown at the bottom and the ordinate scale i s at the lower l i f t edge. Datum planes for hooizontal and vertical distances are shown in Figure 58. Near Drains No. 1, 2. and 3 part of the water-table profiles is missing because the water table in the sand tank was below the ground-water table measuring we:Is.
Streak-Line Tests Investigating Direction of Water Movement Through the Sand
In F~gure 8 a series of photographs show the f~rs t streak-line tests. Bottoms of the photographs are parallel with the sand tank bottom. The recharge rate i s 10 mllsec. This sequence of photographs shows progressive movement of the dye traces. Streamlines of water ilow are shown by the dye traces. The streak-lines show the path of water movement of the recharge, after it enters the water table, and flows toward the drains. The last photograph was taken after completion of the test. Lines were drawn w ~ t h a grease pencil on the sand tank sides.
different types of flow systems present in the sand tank-one flow system where recharge enters the water table and flows into the drains and the second flow system where water moves downslope and passes beneath the drains. Therefore, one objective of the streak-line tests was to visually distinguish and 'show the two different flow systems. Streak-line tests showing the first flow system were done between Drains No. 6 and 7, Figure 9. The photographs were of the grease penciled lines made a t the completion of the tests. Streak-line tests showing the second flow sy;tem were shown between Drains No. 8 and 9 and partially between Drains No. 7 and 8. Figure 10.
Figures 11 and 12 were photographs of streak.lines that illustrate topics in the discussion and analysis part of the report.
Pressure Measurement Tests
Equipotent~al lines, resulting from the pressure tests, are shown on Figures 14, 15, 16. and 17. The sand tank slope and recharge rate are labeled beneath each diagram. For the various tests, contour lines of equal pressure or equ~potential lmes were drawn through the pressure measurement data points. There lines were drawn by mspection and were labeled in thousand:hs of a foot of water. Also shown on the figures are the visualized paths of water movement through the sand.
The water-table profiles for the 0 percent slope tests are shown as solid lines. These profiles, were determined from pressure measurements made at the piezometric taps (row 1 of the form shown in Figure 13A) which were 2 f t above the sand tank bottom. Water-table profiles for a l l the other tests are shown as dashed lines. These profiles were not determined from the pressure measurement data but from the water-table profile data shown in Figure 6. The water-table profiles between Drains No. 4, 5. and 6 were plotted with respect to the sand tank bottom.
DISCUSSION AND ANALYSIS OF TEST RESULTS
Zero Percent Slope Tests
' Interior drain discharges-Water-table profiles and drain discharges are shown on Figure 6 for the 0 percent slope tests. The upper set of curves were for a 12-ft (3.66ml drain spacing and the lower set for a 6-f t (1.83.m) drain spacing. A t 0 percent slope the drain discharges should be equal to the amount of
water applied between two operating drains. For the 12-ft 13.6E-m) drain spacing tests the drain discharges were approximately rwice the recharge rate since there are two recharge units per drain. Therefore, drain discharge percents are nearly 200 percent. For the 6-h (1.83-m) drain spacing ~ests, discharges from the interior drains, No. 3 to 8, were approximately equal to the recharge rates. Discharge from the drains was approximately equal to the quantity of water applied betweenathe operating drsins. The maximum deviation of the drain effluent from the recharge rate was 8 percent. The deviations were attributed to the inherent error present in the sand tank system.
Water-table profiles.-The water-table elevation midway between the drains increased linearly with the recharge rate for both the 6- and 12-ft (1.83- and 3.66-m) drain spacing tens (Figure 18). For the 6.h (1.83-ml drain spacing the midpoint water-table profile elevations between Drains No. 3 to 9 were averaged and for the 12-ft (3.66-ml drain spacing the midpoint water-table profile elevations between Drains No. 2 to 10 were average.
Also shown on Figure 18 were midpoint water-table elevations computed using the Dupuit-Fcrchheimer assumptions'. These assumptions are:
(11 The point velocity along the water-table interface is proportional to the slope of the water table.
(2) The flow is everywhere horizontal.
(3) The velocity i s uniform below the water table.
Using these assumptions, an equation of the form
can be derived. This equation was solved for H, where
The computed midpoint water+table elevations were considerably lower than the measured midpoint water-table elevations obtained from the tests.
Comparisans of some computed and measured water-table profiles are shown in Figure 19. The Dupuit-Forchheimer assumptions were used for the computed profiles. The equation .l~sed for making the computations was similar to equation (2). but in a slightly different form. The equation was:
<> :- ..-;. 2 vx(S - X) y + 2 d y = r . (3)
where the sym60is were the same as previously defined, except for x and y, . ~ . ~ . . . .
y =vertical distance of a given point on the water-table profile above the drain centerline, ft
x = horizontal distance of a given point on the water-table profile from the drain centerline; ft
The solid lines with data points were the measured profiles and the dashed iines were the computed profiles. Figures 19A and 196 were for the respective 12- and 6-ft (3.66. and 1.83-m) drain spacing tests. In all cases and for a given test condition the computed profiles were lower than the measuced profiles. The Dupit.Forchheimer assumptions do not accurately define water-table elevations for the sand tank tests where there was a convergent pattern of water flowing into the drain envelope.
For flow convergence into a drain a correction or adjustment can be made to the Dupit-Forchheimer assumptions. The adjusted d volue in equation (3) provides a more accurate water-table elevation2.
Equilibrium in the Sand Tank
The idea or concept of equilibrium as discussed in this report means the discharge from a given drain is equal to the amount of water applied between two operating drains. In a sense the drain discharge was at equilibrium with the recharge. For illustration, the drain discharges and water-table profiles shown on Figure 7 will be discussed using drain discharges and percents for the 2-112-mllsec recharge rate test. A t the upper end of the sand tank the water table was below Drains No. 1 and 2, therefore, there was no flow from these drains. The recharge between Drains No. 1 and 2 was flowing down slope, through the sand tank, and passing beneath Drain No. 2. The recharge between Drains No. 2 and 3 had raised the water table and the water table was just barely up to Drain No. 3.
S =horizontal distance between operating drains, feet
k =coefficient of permeability, ft/sec v = infiltration rate. recharge rate
divided by 12-foot area the recharge water acted upon, ftlsec
d =vertical distance from the drain center- line to the impermeable barrier, f t
H = distance of the water-table profile above the drain centerline midway between two operating drains, f t
' Luthin, James N., Drainage Engineering, John Wiley &Sons, Inc., p 153, 1966. 'Carlson, E. J., Drainage From Level and Sloping iand, REC-ERC-71-44, US. Bureau of Reclamation, December 1971.
The percent (18.0 percent) of discharge war very small. The recharge between Drains No. 3 and 4 made a further increase in drain discharge. The discharge percent was 96.8 percent. From Drains No. 4 through 9 the drain discharge was approximately a t equilibrium with the recharge.
The same trends are observed in the drain discharges and percents for the 5.. 7-112.. and 10-mllsec recharge rates shown on Figure 7. Drain discharge increases as one progresses from Drain No. 1 to Drain No. 4. Along the midslope of the sand tank [Drains No. 4 to 9) the drain discharge was a t equilibrium with recharge between drains. The drain discharges listed in Table 3 also exhibit equilibrium for tile various tests.
Effect of Slope and Recharge Rate Upon the Water Table Profile
Change of the water table profiles for a constant recharge rate and different slopes.--Figure 20 shows the water table profiles between Drains No. 6 and 8 for a recharge rate of 5 mlisec and a 12-ft (3.66-m) drain spacing.. Drains No. 6 and 8 were selected because the drains were located within the midslope or the equilibrium portion of the sand tank. Also the drains were far enough up slope from end Drain No. 11 for the water table profiles to be negligibly affected by Drain No. 11. The datum of reference for Figure 20 is the centerline of Drain No. 8. The origin i s located a t the lower right corner of the figure. Water table profiles and the location of Drain No. 6 are plotted with respect to Drain No. 8. These plots were made for the five different test slopes. A "V" or pointer on each water-table profile designates zero slope of the water-table profile. Therefore, it is the dividing point for waterfiow into Drains No. 6 and 8. Recharge entering the water table left of the pointer flows into the up slope Drain No. 6 and recharge entering the water table right of the pointer flows into the downsiope Drain No. 8. For the 0 percent slope water-table profile the "V" or dividing point is approximately midway between Drains No. 6 and 8. Progressively increasing the sand tank slope moved the dividing point to the left. This trend was observed with other recharge rates and also for the 6-ft (1.83-m) drain spacing tests.
Change of the water-table profiles for a constant slope and different recharge rates.-Figure 21 shows the water-table profiles between Drains No. 6 and 8 for a slope of 2-112 percent and 12-ft 13.664 drain spacing. The datum of reference for Figure 21 is the centerline of Drain No. 8. Progressively increasing the recharse rate moved the location of the dividing point to the right. This observation is valid for the
other slopes and also for the 6- i t (1.83-m) drain spacing tests.
Change o f the waterfable profiles with respect lo the sand tank bottom.-Another way' of comparing differences between horizontal and ,?he various sloped water-table profilcs was to plot the water-table profiles normal to the sand tank bottom. Figures 22 to 25. The ordinate scale is the distance of the water table measured perpendicular above the bottom of the s a y l tank. The abscissa scale is the station location 2 feet along the sand tank where the water-table measurement was made. Water-table profiles are shown for different slope tests but for the same recharge rate. The water-table profile represented by the line is for the 0 percent slope tests and symbols deignate the 2-112. 5. 7-112, and 10 percent slope profiles. Drain discharges and drain discharge percents are also. shown on the :;rd!-es.
In considering the water- able profiles for the 2-112-mllsec recharge rate shown in Figure 22, two observations were noted:
(1) Fcr the up slope portion of the sand tank. increasing the percent slope caused the water surface profile to be displaced farther down the slope with respect to the 0 percent slope water-table profile.
(2) For the equilibrium portion of the sand tank, water-table pd i l e s were approximately rhe same for the 0, 2.112, 5, 7-112, and 10 percent slope tests. There were deviations of the water-table profiles about the 0 percent slope water-table profile, but the deviations were such that no distinguishable trend was found for water.table profiles of one particular test.
For larger recharge rates, Figures 22 and 23, it was also noted that;
(3) For the up slope portion of the sand tank. ~ncreasing the recharge rate caused the water-table profiles to be displaced further up the slope with respect to the 0 percent water-table profile.
Smla r observations were r.oted for the 12-ft (3.66-m) drain spacing tests, Figures 24 and 25.
Effect ot Slope and Recharge Rate Upon Drain-Discharge
General.-In the equilibrium portion of the rand tank, the slope or recharge rate had no effect upon
the drain discharge. The drain discharge was approximately equal to the water applied beween operating drains. Only near the sand tank ends were the drain discharges affected by the slope and recharge rate.
Change of drain discharge for a constant recharge rate and different slopes.-For a given recharge rate, increasing the sand tank slope increased the discharge from the lower end drain (No. 11) while the discharge from drains near the upper end decreased. For example, with the 2-112-mltsec recharge rate tests and 6-ft (1.83-m) drain spacing, Figure 22, the discharges from Drain No. 3 decreased as the slope increased. The 10 percent slope affected discharges from drains as far downslope as the No. 4 drain. Whereas, at the downslope Drain No. 11, increasing the slope increases the drain discharge from 74.4 to 364.0 percent.
The effect of slope upon drain discharges is not as great with higher recharge rates. A t the l0.mllsec recharge rate (6-ft ( 1 . 8 3 4 drain spacing. Figure 23) discharges from Drains No. 3 and 4 were not significantly affected by the 10 percent slope. Similarly, the difference between discharges from Drain No. 11 were less at rhe IO.ml/sec recharge rate. The drain discharge increased from 67.6 to only 145.4 percent.
Change o f drain discharge for a constant slope and different recharge rates.-For a given sand tank slope, increasing the recharge rate increases the disct qe from both the lower and upper end drains, Figure 7. However, there was a contradiction beween drain discharges and drain discharge percents for end Drain No. 11. As the recharge rate increased the drain discharge increased, but the drain discharge percent decreased.
Streak-Lines and Direction o f Water
velocities the streak-lines are thinner. For example water velocities are higher neir the drains because of convergent flow. A t low velocities the streak-lines are thick., There was more time for the dyed water to diffuse. The dividing point streak-line at the middle part of the left plexiglass panel had a very slow velocity. This streak-line originates 5.112 grid spaces to the left o f the center post below the clock. Note the grid distance travel beween the 5- and 17-hour photographs. Recharge left of the dividing point streak-line flows upslope into Drain No. 7. This dividing point streak-line emerged from the zero slope point of the water-table profile.
Streak-line tests were made with four recharge rates with a 2-112 percent slope. Figure 9. Photographs were taken after completion of the tests. Paths of the streak-lines were grease penciled upon the sari? tank sides. For a constant slope, the effect'of the recharge rate upon the flow system was observed. With decreasing recharge rates the dividing streamline moves up slope, to the left and closer to Drain No. 6 in the photographs. Also when the recharge rate was decreased the recharge flow area decreased.
A similar series of tests were made to define the area in which water passed beneath the drains, Figure 10. Some streak-lines o f water passing beneath the drains may be seen beween Drains No. 7 and 8. Beween Drains No. 8 and 9 an effort was made to completely dye the area blue where water was flowing downslope beneath the drain. Aga~n it can be observed that with decreasing recharge rates the flow area o f the water passing beneath the drains increases.
In the sand tank tests equilibrium. did not exactly occur. There were slight differencecamong the drain discharges along the midslope portion of the sand tank. In reality some recharge between drains would escape into the flow system of water passing beneath the
Movement Through the Sand Tank . ' ,:: drains. For other drains water was drawn from the flow system of water passing beneath the drains. Figure 11
Figure 8 shows the results of the first streak-line test. shows one o f the streak-line tests where recharge water These photographs are of the flow system where escaped into the flow system of water passing beneath recharge water enters the ground-water table and then the drains. flows into the drains. Some properties shown in this test are typical of the other three streak-line tests. Dye The effect o f the end drain envelope upon streakjines ---.:-~. .. forming the streak-lines was introduced at the 2-ft of flow entering Drain No. 11 was also observed;' (0.61-m) level in the sand tank (centerlineelevation of Figure 12. The streak-lines, while in the fine aquifer the drains). The streak-lines originating near the drains sand, f low parallel along the sand tank bottom and flow neariy parallel with the sand tank bottom and then into the end drain envelope. The streak-lines do
case where streak-lines of recharge entering between drains escape into the flow system passing beneath the drains. The dark strip along the sand tank bottom is the dyed water from beneath Drain No. 8.
Pressure Measurement Tests
Zero percent slope tests.-Results of the 0 percenr slope pressure measurement tests are shown on Figure 14. Theoretically the equipotential lines should be symmetrically located with respect to a vertical line midway between the drains. However. results of the pressure measurement data are not exactly symmetrical. For example, the shape of the 100- thousand th - foo t equipotential line is unsymmetrical between Drains No. 4 and 5. Two explanations for deviation of the measured potential field with respect to the theoretical potential field are; (1) the recharge water applied to the sand surface was not exactly uniform, and (21 the sand or porous medium was not exactly homogeneous.
Permeability variations were noted within the sand tank. For example, streak-line below Drain No. 7 (Figure 11) shows one such variat~on. Therefore. streamline patterns were not superimposed on the equipotential lines because of the recharge and permeability dev~ations. Instead o f drawing an exact flow net, arrows are drawn perpendicular to the equipotential lines. There arrows show the visualized path of water movement through the sand.
2-7/2percent slope tests.-Results of the four 2-112 percent slope pressure measurement tests are shown on Figures 14 and 15. The heavy lines, with arrows, separate the two different flow systems. Results of the corresponding streak-line tests were used as an aid for locating the heavy lines. Below the heavy line the flow system of water moved downslope and passed beneath the drains. Above the line the flow system consisted of recharge water which flowed into the drains. The upper flow system i s divded into two parts, recharge flowing into the downslope drain and recharge flowirig into the up slope drain. The point where the f low systems intersected is shown by dashed lines, since this intersection point is not readily defined. The change in stream potential occurring at the intersection point i s small. This can be seen from the wide spacing o f the equipotential lines near the intersection point. Another factor contributing to the indeterminate nature o f the intersection point i s the absence o f pressure data immediately downslope from the
. ~
drains, Figure 13A.
5, 7-1/2 and 10 percent slope tests.-Results of pressure measurement tests made at the minimum and max~mum recharge rates for the 5, 7-112. and 10 percent slopes are shown on Figures 16 and 17. The effect of varying slope and recharge rate upon the potential field may be observed. Increasing the slope for a given recharge rate produced a larger number o f equipotential lines for the same contour interval. Higher downslope velocities occurred in the sand tank because of the increased slope. For pressure measurements made in the sand tank a small slope increase (from 0 percent slope) greatly influenced the potential field between drains. For instance, at the 0 percent slope a large area between drains contained equipotential lines with a horizontal-type inclination, but at a 2.112 percent., slope the area between drains mostly containec: equipotential lines with a vertical-type inclinatio,<:l
,\ There is a further increase of the vertical inclination' for the equipotential lines at the 5 percent slope. The slope changes to 7-112 and 10 percent did not affect the potential field (with respect ' t o horizontal-type equipotential lines) nearly as much as the 0 to 5 percent slope changes.
Increasing the recharge rate for a given slop,p:altered the potentiai field near the drains. With the 2-112-mllsec recharge rate the equipotential lines were somewhat evenly spaced. Figure 17. However, - at the l0.mllsec recharge rate the equipotential lines are unequally spaced. Here, the lines are closer together up slope from Drain No. 5 and farther apart downslope.
With the exception o f the 5 percent slope and a 10-mllsec recharge rate test the potential field was not well enough defined to determine the intersection point and to show the two flow systems.
Influence of the End Drain Envelopes
Comparison of ,flow into an interior and an end drain.-The envelopes for the two end drains (No. 1 and 11) were different than envelopes for the interior drains. For the interiordrains there was a circular envelope around the dra~ns,:Figure 1. This created a donverging pattein of streamlines en tehg the envelope, Figure 26A. For the most part the pattern of converging stl-eamlines occurred in the fine sand. Thus, the closer the particle of water was to the drain the higher the velocity and the higher the friction or headloss.
For the two end drains, the envelopes extended 0.5 f t (15.0 cm) from the ends of the sand tank and
from the b ~ t t o m of the sand tank to the top surface. The pattern of streamlines entering an end drain envelope consisted of a somewhat parsllel or horizontal pattern. Then the streamlines traveled vertically upward in the envelope and into the end drain. Figures 12 and 26A. Waterftow into an end drain envql~pe more closely resembled the Dupuit-Forschheimer assumptions than the converging-type flow entering and interior drain envelope. Furthermore, the permeability of the medium-size sand was greater than permeability of the fine sand. Thus, from Equation 1, one can infer that there was less headloss occurring for a given flow entering an end drain than for the same flow entering an interior drain. Therefore, an end drain envelope is more efficient for drainage.
Zero-percent slope tests.-If flow conditions for the end drains were similar to the interior drains, then the end drain discharge should be about 50 percent of the recharge rate. However, the tests showed that the end drain discharges were always greater than 50 percent, Figure 6. In addition, the water-table profiles were lower than the corresponding interior drain profiles. These differences were probably due to the greater efficiency of the end drains. The flow rates from the two ends of the tank were not equal. Probably the unequal distances between Drains No. 1 and 2, and Drains No. 10 and 11 accounted for the differences of profiles and discharges of the two end drains.
The water-table profiles were measured and computed between Drains No. 10 and 11, Figure 19C. Equation 3 of the Dupuit-Forchheimer assumptions was used t o obtain the computed water-table profiles. The drain spacing distance (S) used was 8 f t (2.44 m) instead of 6 f t (1.83 m) since Drain No. 11 acted upon a greater distance than one-half the 6-ft (1.83-m) drain spacing test distance. The effect of Drain No. . l l can be seen by e::amining the measured water-table profiles which show the point of 0 percent slope to be approximately 4 feet (1.22 m) lef t of the drain. Agreement between the computed and measured profiles for Figure 1?C was considerably better than for the interior drain-$ ~1;Figures 19A and 198.
. .. ~
Twelve-foot drain spacing tests.-The purpose of the controlled tests was t o isolate or eliminate the effect of the end drain envelope upon drainage up slope from end Drain No. 11. A t end Drain No. 11 the water-table profile was raised, Figure 268. The controlled water-table profiles between Drains No.
the added pressure at end Drain No. 11 the efficiency of the end drain envelope was somewhat reduced.
The controlled and free flow tests provide information about how far up slope influence of the end drain envelope effect'qxtends. Figure 27. As one progresses up slope the dtfference between the controlled and free flow profiiks becomes less. For the 2-112 percent slope, the c o : h l e d and free flow profiles were approximatelythe same a t Drain No. 8. Results of the w,atsi%&le profiles for 5, 7-112. and 10 percent s106e tests were similar t o the 2.112 percent slope tests. In addition to similarities in water surface profiles, at Drain No. 8 the controlled and free flow discharges were practically the same. Therefore, it was concluded that for free flow tests
-
influence o f the end drain envelope did not extend up slope past Drain No. 8.
Six-foot drain spacing tests.-No controls were imposed upon Drain No. 11 for the 6-ft (1.83-m) drain spacing tests. However, conclusions could be reached about the distance up slope which was
, affected by the end drain. For Drain No. 9 all the discharges were approximately equal to the equilibrium discharge. Table 3 and Figuies 22 and 23. For Drain No. 10 the discharges were less than the equilibrium discharges. Thus, it was concluded .- that the influence of the end drain envelope J!
affected discharge from Drain No. 10, but had an k' insignificant effect on Drain No. 9. Thus, the ,,;Y
?' influence of the end drain envelope upon the water-table profiles was assumed not to extend up;, slope beyond Drain No. 9. . .
Flow o f Water Downslope Passing Beneath the Drains
A study was made to determine what affect changes in percent slope, recharge rate, and drain spacing had ~'
upon the flow of water downslope passing beneath drains. For this study an inventory was made using the drain discharge data in which the amount of water flowing downslope ~ n d passing beneath the drain was computed for each drain. Figure 28. The flow values were averaged for each t e s t and they represent an ' ,
I equilibrium condition of drain discharge. Table 4 and Figure 29. Drains that were considered not t o be in equilibrium were excluded in the averaging. For example flow values for Drains No. 1, 2. 3, 4. and 10 !
were not used. Similarly. with the 12-ft (3.66-m) drain spacing tests the flow values for Drains No. 2, 4, and I
10 were not used. The effect of the s lo~e and recharae
increasing the sand tank slope increased the flow of water downslope that was passing beneath the drains, Figure 29A. On the other hand, for a constant slope an increase in the recharge rate,decreased the downslope flow passing beneath the drains, Figure 298. However, the percent slope variable appeared to have tne strongest influence on the downslope flow. As the slope varied there was a six-fold change in the downslope flow. Whereas, the recharge rate variations were 3/10 or less, depending upon the percent slope, Figure 298. Two (Sldl ratios were used in the tank tests,
(1) S/d = 6 fo r 12-foot drain spacings (2) S/d = 3 for &foot drain spacings.
For a given recharge rate and percent slope, there is less downslope flow passing benea:h the drains when S/d = 6. Figure 29A. Evidently different (Sld) ratios cause variations in the flow patterns below the drains.
Developmmt of Water Movement Beneath Drains
General.-TI& streak-line tests (Figures 9, 10, and 111 and the pressure measurement tens (Figures 14, 15, 16, and 17) show a complex pattern of water movement beneath the drains. An understanding of how the recharge rate and slope affect the flow beneath a drain may be helpful for interpreting the sand tank test results and for analyzing drainage conditions other than those tested in the sand tank. The dexription of the flow conditions occurring beneath the drains is of a hypothetical character. In the following dexription the (S/d) ratio is held constant.
Constan recharge rate and effect o f slope changes.-Water movement toward a drain wil l be considered first for a 0 percent slope. Figure 30A. The velocity change that occurs along a given vertical and horizontal plane will be examined. The vertical plane is from the Stagnation Point C to the drain. The horizontal plane is on the sand tank bottom between the Stagnation Points C and P. A particle of water has a relatively low velocity near[&. the stagnation points. Due to convergence of flow '' into the drain, the velocity along the vertical plane beneath the drain continually increases from Point C to the drain. Along the horizontal plane the direction of water movement is to the left and the maximum velocity occurs somewhere beween Stagnation Points C and P. Also if the recharge rate is increased there will be a proportionate increase in the velocities along the vertical and hoqzontal planes. i f
altered, ~ i g u r e 308. Because of the tilt'there is a downslope or downhill force acting upon the system. Even though the W o planes are no longer vertical or horizontal the planes will still be referred to as the vertical and horizontal planes. There are now W o ~elocit$\,~ components along the vertical:' plane. One velocity component is still parallel wi ih the vertical plane. The second velocity component acts downslope and is perpendicular to the vertical plane. Along the horizontal plane the downslope velocity component is parallel with the plane and acts in a downslope direction. Therefore upslope velocities acting along the horizontal plane wil l decrease. The pan of the horizontal plane influenced the most by the downslope velocities are the areas near the Stagnation points C and P. As the slope increases, the Stagnatibn Point C is located farther downslope at C'. The Stagnation Point P has . moved upslope to P'.
"I" and two flow systems are established. Figure 318. The boundary line between the two flow systems can be thought of as an envelope curve enclosing the flow system to the drains.
I f the recharge rate is increased the upward velocity component along the vertical plane (Point C-Drain) is increased. Also, the downslope velocity component acting along the envelope isaffected by an increase in the recharge rate. An increase in the recharge rate-forces the envelope closer t o the bottom of the sand tank, Figure 31C. This results in a decreased flow area for the flow system of water passing beneath the drains. The Stagnation Point ,, r , . I is farther downslope and closer to the sand tank bottom.
In general for a constant slope, increasing the recharge rate decreases the flow passinq beneath the drains, Figure 298.
Location of the First Upslope Drain
General.-One problem arising in the installation of agricultural drainage systems on sloping land is location of the first up slope drain. For instance, if a
,~
drain is located too far up slope it wi l l never .'
function. Actually the sand tank tests were not oriented toward this type of an investigation, bu: an approximate method was found to locate the first up Slope drain. General results or observations of the sand tank tests were used in developing the approximate method. In reality the location of the first up slope drain, obtained by the approximate method, is too far down the slope. Factors, such as (11 the existing up slope waterflow conditions and (21 the varying quantity of downslope flow passing beneath a drain, can cause the first drain location to be further up the slope. Therefore, the approximate method provides only the lowermost downslope location t o be considered in placing the first up slope drain. Engineering judgment must be used to obtain a n&e:accurate location for the first up slope drain.
Emp i r i ca l development of the approximate method.-For the sand tank tests a conslstant trend in the drain discharges was noted at the upper end of the sand tank. T b discharge of each succeeding downslope drain increased until the equilibrium area of the sand tank was reached. In the equilibrium area of the sand tank all the drain discharges were approximately the same. Therefore, the objective was to position the first up slope drain a t a location where discharge from the drain would be approximately equal to the equilibrium discharge.
An example that illustrates the interpretation of a sand tank test for locating the first up slope drain can be found with the 2-112-mllsec recharge rate, 7-112 percent slope. and 6-ft (1.83-m) drain spacing test, Figure 7. Drains No. 1 and 2 were not operating. Drain No. 3 was operating only at a partially optimum discharge, 0.45-mllsec. An optimum discharge was assumed to be equal to the equilibrium discharge, or for this specific test 2-112 mllsec. Therefore. Drain No. 3 was not used at full capacity. Drain No. 4 had a 2.42-mllsec discharge. For this specific test the most probable location for a hypothetical first up slope drain in the sand tank would be between Drains No. 3 and 4 with the location closer to Drain No. 4 than to Drain No. 3. By visual inspection a good location for the first up slope drain appears to be approximately 16 f t (4.88 m) from the upper end of the sand tank.
..
Another rational meth<.f&r placing the first up slope drain would be to' locate it one drain spacing downslope from the point where the water table crosses the depth at which the drains are placed. For example, use the same 2-112-mllsec recharge rate, 7-112 percent slope. and 6.ft (1.83-m) drain spacing
. . test, Figure 22. A t a position 10.5 ft (3.2 m) from - t h e upper end of the sand tank the water tsble
crosses the 2-ft (0.61-ml depth. I f the first up slope drain was located one drain spacing distance of 6 f t downslope from the 10.5-ft position, the downslope distance for the first'up slope dr?in would be 16.5 f t (5.03 m). This compares favorably with the 16-ft ( 4 . 8 8 4 distance made by the visual inspection. The location where the water table reached a 2-ft elevation (centerline elevation for the drains) was considered a very helpful and significant aid for indicating the location of the first up slope drain.
Description of h e approximate method.-An approximate computational procedure was developed to locate the first up slope drain. The computat ional procedure considers slope. permeability, recharge rate, and the depth of the aquifer, which is assumed equal to the perpendicular distance from the impermeable barrier to the drain centerline. The computational procedure is based on the distance needed to accumulate a recharge which is equal t o the downslope flow. Very idealized and simplified conditions of water movement were assumed when making the downslope flow computations. The following conditions (similar t o Dupuit-Forchheimer assumptions) were assumed: (11 the downslope flow is parallel with the sand tank bottom, and (2) slope of the water-table profile producing this water movement is equal to the sand tank slope. These assumptions are contrary
t o the actual flow conditions which occurred, in the sand tank. The downslope flow was not birallel with the sand tank bottom. In addition,', the assumed water-table profile slope was probably;too large. Therefore, the approximate method gives'the location of ::4e first up slope drain too 'far downslope. "
The quantity of downsiope flow is computed using Equation (1). The following example computation was made using s 2-ft (0.61-m) depth, 7.112 percent slope, and 2-112.mlIsec recharge rate:
Downslope Flow
Recharge rate changed to ft3/sec
Recharge rate per linear foot of sand tank
(0.1472)10-% ft-sec
Length needed for accumulated rccharge to equal downslope flow
ft-sec
Add 6 ft (1.83 m) (drain spacing distance) t o the 11.54 f t (3.52 rn) and then by the approximate method location of the first up slope drain is 17.54 f t (5.35 m) from the upper end of the sand tank.
Comparison of the approximate method for locating the first up slope drain with results of the sand tank tests.-Location of the 2-ft (0.61-m) water-table elevation (drain centerline elevation) was the criterion for making the comparison. The distance of t he 2 - f t elevation determined by the computational procedure was compared with the location of the 2-ft elevation in the sand tank. Using the computational procedure, distances were computed for recharge rates of 2-112.. 3.. 4, 5.. 7-112-, and 10mllsec recharge rates at each percent
slope. Figure 32. For the varlous sand tank tests, distances of the 2-ft water-table elevation were determined from Figures 22 t o 25. The data were plotted on Figure 32.
In general, the sand tank tens *onfirmed that the computational curves of the approximate method located the first up slope drain too far down the slope. The one exception was the 6-ft (1.R3-m) drain spacing test with the 10 percent slope and 2-112-ml/& recharge rate. The largest difference between the 6-ft drain spacing test c h p and the computat ional curves was 2-11? ,ft, or approximately two-fifths the drain spacinyf~stance. For the 12-ft (3 66-m) drain spacing ter;fs, the ' largest difference was 2.112 fP (0.76 m) or approximately one-third of the drain spacing distance. The maximum difference for both drain spacings occurred with the 2-112 percent slope tests.
\
~f the sand tank. This equilibrium condition was defined such that d~scharge from a drain was approximately equal t o wder applied between two operating drains.
2. Within the limlts of experimental error, the water-table profiles measured perpendicular to the sand tank bottom for a give1 recharge rate were almost identical for slopes between 0 and 10 percent. This occurred in the equilibrium area of the sand tank.
3. There were two distinct ground-water flow systems within the equilibrium area of the sand tank. The recharge flow system consisted of recharge water entering the water 'table moving partially downward into the sand tank, and then flowing into th? drains. The downslope flow system consisted of water which moved downslope below the recharge flow system.
4. The predominant area of the two flow systems were affected by slope and recharge. Holding the recharge constant and increasi~g the slope decreased the area of the recharge flow syszem. Holding the slope constant and increasing the recharge rate increased the area of the recharge flow system.
5. Drainage characteristics for the end drains were diffejant from the interior drains of the wnd tank due to design differences of the envelopes. The end drain envelope extended down to the sand tank bottom. The Dupuit-Forchheimer assumptions better simulated water flowing toward the end drains than it simulated the convergent pattern of water flowing toward the interior drains.
APPLICATIONS
The investigation was for steady state flow and of a general nature. No conditions for a specific geographical location, such as permeability, dimensions o f drains or envelopes, distance between drains. distance from the drain to the impermeable barrier,
additional studies would be required. However, results from this research study will help drainage engineers obtain a better understanding about flow conditions in the porous media for agriculttlral drains on sloping land. I n addition, approximate methods for determining the location of the first up slope drain on sloping land are included.
\
Results of the investigation indicate that sloping drainage has aspects similar to drainage for 0 percent slopes. Therefore, studies later were made to investigate how well ;he theory and equations for the 0 percent slope conditions would apply to slooing sand tank tests.'
- - .-
NOTATION
The following symbols were used in this report:
d = vertical distance from the drain centerli1.0 to the impermeable barrier, ft:
i = slope or hydraulic gradient, ft l f t : k = coefficient of permeability, ftlsec: v = infiltration rate, ftlsec; w = 2-foot width of sand'tank. ft: x = horizontal distance of a given point on
the water.table profile from the drain ce"terline, ft:
y = (Equation 1) depth of flow, ft; y = (Equation 3) vertical distance of a given
point on the &er-table profile above :::?,
the drain centerline, ft; A = area of flow,, ft2: H = distance of the water-table profile above
the drain centerline midway between two operating drains, ft:
L = length needed for accumulated recharge to equal downslope flow, ft;
Q = discharge flowing through the sand, ft3lsec;
S = hilrizontal distance between operating drains, ft.
'Carlson, E. J.. Drainage From Level and Sloping Land, REC-ERC-71-44, US. Bureau of Reclamation. December 1971.
Table 1 -
LOCATIONS OF THE GROUND-WATER TABLE MEASURING WEL S
Manometer number
Station Slope in feet distance
I -- Manometer Station number in feet
':: 5.38
8. i 8 .. :.
8.97
Wdnometer Number-Identification number of the ground.water table measuring wells and manometers. Station in feet-The station location where the ground-water table measuring wells were placed along the sand ~ '
tank. The left end of the sand tank (up slb'pe) was Station 0 dnd the right end (downslope) was Station 60.$;:, Slope distance-The distance between the well and manomater.&gative distance shows that the well was up slope from the manometer. Used in computations shownin'Figure 5A.
- . .- . . .. 3 . .>: .... . .
x:. ~,
. ~
. - = .,
-
.., .? ' i _ . .. -
. , " -. . *
.. : ,! . . -. ..,
12-foot drain spacing 12-foot drain spacing 6-foot drain rpacing free flow tests controlled flow tests
Percent Recharge Date Percent Recharge Date Percent Recharge Date slope rate performed slope rate performed slope rate performed I I I I I I
slope 3'
2.112 2-29.68 2-29-68 3- 1-68 3- 1-68
Table 3
DRAlC DISCHARGES
6-foot Drain Spacing - Drail -
Discharge - 2.30 4.38 6.46 8.63
1.76 4.42 6.56 8.80
0.05 3.30 6.35 8.60
0.00 1.68 4.70 8.22
0.00 0.00 3.08 8.42 -
-- 0.3 Percenf recharge -
92.0 95.2 97.6 99.0
88.0 91.0 92.3 93.8
76.4 90.0 92.9 94.5
18.0
Drail --
Discharge -- 2.30 4.76 7.32 9.90
2.20 4.55 6.92 9.38
1.91 4.50 6.97 9.45
0.45
Ill Drain d8rcharger aregiven in ml lm. 12) Percent recharge is the drain dirharge expressed ar a ~ercent ol f the
$
-
discham rate from one recharge unit.
Drain No. 11 -
Total drain
discharges - 25.28 49.64 74.65 99.79
24.72 49.23 73.99 99.63
23.85 47.50 71.35 96.91
54.80 49.48 73.84 98.98
24:14 46.32 71.72 96.64 -
Drain No. 6 Urair
Dizharge - 2.60 4.96 7.30 9.64
2.52 4.85 7.25 9.60
2.49 4.65 6.80 9.16
2.60 4.94 7.24 9.77
2.56 4.78 7.00 9.40 -
Drain Drai - lischarg - 2.52 1.77 7.36 9.80
2.311 4.75 7.20 9.70
2.37 4.85 7.00 9.40
2.38 4.66 7.20 9.65:
2.38 4.82 7.10 9.60 -
recharge - 74.4 70.0 68.3 67.6
152.0 117.2 96.4 92.0
224.0 149.0 123.5 110.0
298.0 183.6 149.3 128.6
364.0 217.6 188.5 145.4 -
Conditmn Drain No. 11 --
Free flow
Flee llaw
Contro<od flow
Free flow
Controlled flow
Free flow
Controlled flow
Free flaw
Controlled flow
Recharg rate -
2.112 3 4 5
2 112 3 4 5
2 112 3 4 5
2.112 3 4 5
2 112 3 4 5
2.112 3 4 5
1112 3 4 5
3 4 5
3 4 5
- Drai -
lirharg - 5.05 6.02 7.96 0.02
2.80 3.83 5.76 7.80
2.87 3.88 5.80 7.82
0.96 1.90 3.76 5.89
0.85 1.80 3.78 5.80
0.00 0.48 2.37 4.14
0.00 0.14 2.23 4.30
0.W 0.18 2.06
0.ooi: 0.18 2.30
- Percent recharge - 192.0 191.7 190.7 197.4
182.4 186.7 190.0 189.4
178.8 188.7 187.5 189.6
176.0 180.0 185.0 188.0
174.8 176.0 183.0 185.0
174.0 195.3 200.5 2W.O
156.8 191.7 995.5 197.2
128.7 177.5 182.0
, .
128.7 175.0 178.8
Tsble 3-Caotmued
DRAIN DISCVARGES
12 fool Elam Spamq -- Drai -
Dischag\ - 4.80 5.79 7.78 9.80
4.811 5.60 7.50 9.45
4.62 5.70 7.52 9.42
4.82 5.74 7.50 9.40
4.73 5.63 7.45 9.30
5.12 6.12 8.08 9.97
4.90 5.98 8.00 9.90
5.50 7.50 9-20
5.57 7.60 9.38
- +?- Percent recharge - 192.0 192.7 194.5 196 0
192.0 186.7 187.5 189.0
188.0 I90.0 188.0 188.0
192.6 191.3 187.5 188.0
189.2 187.7 186.2 186.0
204.8 204.0 202.0 199.4
196.0 199.3 200.0 198.0
1833 187 5 184.0
185.7 190.0 187.6
(1) Draln dlrcharger are gwen in rnllscc. (2) Percent recharge is the dram dlrcharge exprerred as a percent of the dlaharge rate from one rechargecmt
& Percent rccharsl - 205.2 201.7 203.8 202.0
126.0 124.0 125.0 128.0
190.4 196.7 198.8 197.2
120.0 103.3 121.2 124.0
194.0 190.7 196.8 i98.0
131.2 129.7 129.5 135.6
196.0 106.7 200.0 202.0
121.0 120.0 124.0
186.7 192.5 196.0
- Drain -
lirchi~rgr - - - - -
3.96 4.30 5.10 5.83
2.04 1.99 2.07 2.18
5.90 6.30 7.W 7.78
3.88 3.98 3.76 3.82
7.65 8.02 8.82 9.50
5.98 5.90 5.78 5.95
9.70 0.50 1.30
7.52 7.50 7.60
- 1_11 Pctcent reclmrgt - - - - -
158.4 143.3 127.5 116.6
81.6 66.3 51.8. 43.6
236.0 210.0 177.0 155.0
155.2 132.7 04.0 76.4
3C6.0 267.3 220.5 190.0
239.2 196.7 144.5 119.0
323.3 Z62.5 226.0
250.7 187.5 152.0 --
Table 4
FLOW IN MLISEC DOWNSLOPE PASSING BENEATH THE DRAINS
5 percent 7-112 percent Test slope 2.11: Test recharge 2-112 ! I
Average recharge 2.472
3 'Aversge flow
'Average obtained from flow beneath Drains No. 4.5. 6,7,8, and 9. -
12-foot Drain Spacing I 5 percent I 7-112 percent I 10 percent
3 4 5 2-112 3 4 5 3 4 5 Average recharge 2.342
2 0.37 4 0.58
Drain No. 6 0.61 8 0.67
10 1 "Average flow
"Average obtained from Drains No. 6 and 8.
Recharge sprinkler over surfoce o f sand tank
D~f ferent ia l
Storage
O r ~ f ~ c e
- Collection tank w ~ t h o f l oa t ,
oc t~vated sw~tch to control the pump
Figure 2A
-D and + D are the slope distances given in Table I.
NA = (Manometer Reading a ) -c NB = (Manometer ~ e a d i n g b ) + c
Fiaure 5A. Water table profiles normal to the bottom of the sand tank.
SW is the station of the ground-water table measuring well given in table I.
NW I S normal distance to bottom of tank, . , A. ( S e e Figure 50, Nw= N A or NB)
D = ( S W ) ( C O S @ ) H = (60'- S W ) (SIN 8 ) v = ( N W ) ( C O S ~ ) R = ( N W ) , ( S I N O )
X = D t R Y = H t V
Figure 58. Trfigonornetr~c computatrons made to correct monometer readmas
Stan of test. Photo PX-D-70794 .,*;.,- ,--.,.,..---..; ;,-
.-&*.. -.-A
. . A-'.'. 7~ .~
112 hour. Photo PX-0-70795
1-112 hours. shot0 PX-D-70796
5 hourr. Photo PX-D.70797
6.314 hours. Photo PX-G-70798
12 hours. Photo PX-0.70813
c--- ..-.. .. . . a -,.~.p.,:* s- .- I . !
-
17 hourr. Photo PX-0.70814
22-314 hours. Photo PX.3.70815
33-112 hours. PhotoPX-0-70816
---- "
Cornplet~on of test Photo PX.D-70817
Figure 8. Streak-line tests showing formation of streamliner. Slope 2-112 percent-Recharge rate 10 rnllsec
3 1
Recharge rate 10 rnllrec. Photo PX-D-70800
Recharge rate 5 rnllsec. Photo PX-0.70807
, . i..,. 6~1 4,. . . . I .
I,.. ., ,i . 3 I-- . .-
. . Recharge rate 2.112 rnllrec. Photo PX-D-70811
Recharge rate 10 mllsec. Photo PX-0-70799
Recharse rate 7.112 mllsec. Photo PX-D-70804
. . "; -- . 2 % ~ .~ . .
Recharge rate 5 rnllrec. Photo PX.D-70808
Recharge rate 2-112 mllsec. Photo PX-D.70810
Figure 10. Streak-line tests rhowing the flow system of water parring beneath the drains-&foot drain spacing and 2-112 percent slope.
DRAIN NO. 4
\ \ O
0 P E R C E N T S L O P E 5 ml/sec RECHARGE R A T E
H D I S T A N C E IN F E E T ABOVE T H E D R A I N C E N T E R L I N E
0 ? 0 - N W
12-Foo t D r a i n Spac ing ond 5 mvsec . Rechorge R o t e I I
i ~ r a i n No. 6 '0 % Slope
2 % % S l o p e 0 5 % Slope
! 10 9 8 7 6 5 , .. 3 2 0
DISTANCE IN FEET LEFT OF DRAIN NO. 8
Figure 20. Water table profiles between Drains No. 6 and 8 by slops. -
1 2 - - F o o t D r o ~ n S p a c i n g a n d ' 2 V t % Slope
i e
r a t e ml sec. R e c h a r g e r a t e m l sec. R e c h a r g e r a t e
e m l sec. R e c h a r g e r o t e
I v P o i n t of zero slope on t h e
w o t e r t a b l e p r o f i l e
9 B 7 6 5 3 3 2 I
DISTANCE IN FEET L E F T OF DRAIN NO. 8
Figure 21. Water table profiles between Drains No. 6snd 8 by recharge rete.
INTERIOR DRAIN END DRAIN
Figure 26A. Diagram showing streamlines of flow entering an interior and an end drain envelope. Drain envelaper are the shaded area.
Water table profile controlled by small box with overflow weir
Small box with overflow weir
Water toble profile for f ree flow conditions
Flexible tube Distance of water toble profile
normal to bottom of sand tank determined from rnonometer readings of 0 % slope tests
- ..
Figure 268. Diagram showing method for mntroiling height of water table profile near End Drain No. 11.
oran numters 9 9 \P/ \9/ y' Drain p 0 1.76 2.20 2.56 2.32 2.64 2.34 2.52 discharge - - d 4 - 4
Numbers deslgnote flow. expressed In ml/sec Example IS shown only up to droln No 8
Results for dra~ns No 9, No 10 and No 11 are slmllar.
1. Total drain discharge 24.72 mllsec. For 10 recharge umts, 2.47 mllrec per recharge unit. Far the 6Ofoot sand tank length the recharge per linear foot along the tank is 24.72 mllrec + 60 f t = 0.41 2 mllsec-ft.
2. Determine location of the zero slope paint or dividing paint for the water table profiles between drains. Get
i distance between zero rlope point and the uphill drain. The iacation of zero rlope points war obtained from working graphs or large-size plots of the water table profiles which are not included in this report. Dnly the distance for Drains No. 3. 4, and 5 are given for this example. The distances are Drain No. 3-0.78 ft. Drain No. 4--0.99 f t , and Drain No. 5-0.98 ft.
4. Input-output analysls to determine flow of water parsing downrlope beneath the drains.
Drain No. 1. The drain is next to the up-slope end of the sand tank, therefore no flow downslope.
Drain No. 2. Flow into the drain comes entirely from downrlope flow which is the recharge between Drainr No. 1 and 2. (2.47 - 1.761 mllrec = 0.71 mllrec.
Drain No. 3. Flow into the drain comer from 111 flow beneath Drain No. 2 - 0.71 mllsec. (21 downslope flow between Drains No. 2 and 3 - 2.47 mllsac, 131 up-slope flow between Drains No. 3 and 4 - 0.32 rnllrec. (0.71 + 2.47 t 0.32 - 2.201 ml/rec= 1.30 mllzec.
3. Determine amount of water from the recharge unit that Drain No, 4, Flow into the drain comer from flows up slope. the remaining water flows downslope. beneath Drain No. 3 - 1.30 mllsec 121 downslooe flow ~ - ~. . 7 - ~
between Drains No. 3 and 4 - 2.15 mllrec, 131 up-slope flow between Drains No. 4 and 5 - 0.41 mllrec. 11.30 + 2.15 + 0.41 - 2.561 mllsec= 1.30 mllrec.
Drain No. 5 (1.30+ 2.06 t 0.40 - 2.321 mllzec = 1.44 mllrec
Drain No. 6 11.44+ 2.07 + 0.42 - 2.641 mllsec = 1.29 mllsec
Drains No.
3-4
Drain No. 7 11.29+ 2.05+ 0.38 - 2.341 mllsec = 1.38 mllsec
Drain No. 8 11.38 + 2.09+ 0.30 - 2.521 mllrec
0.78 f t x 0.41 2 mllsec-ft = 0.32 mllsec = 1.25 mllsec
(up rlopel 2.47 - 0.32 = 2.15 mllsec (downslopel
0.99 f t x 0.412 mllrec-ft = 0.41 mllsec (UP rlopel
2.47 - 0.41 = 2.06 mllrec-ft (downslopel
0.98 f t x 0.41 2 ml/rec.ft = 0.40 mllsec (UP slope1
2.47 - 0.40= 2.07 mllsec Idownslopel
Figure 28. Example of ~nput-Output analyr~r to determine flow downslope passang beneath the drams.
* 57
'2aS/IUI SWVO 3 H l H l V 3 N 3 8 9NISSWd M o l d 3 d O l S NMOO
' 2 J S / I U SWWO 3 H l H l V 3 N 3 8 9NlSSWd MOW 3d01S NMOO
C
Bottom o f sand tank
P F~gure 31A. Umforrn flow downslope.
Water table prof~ le
DRAIN
--Boundary between two flow systems
-
Bottom of sand tank
Figure 318. Illustration of two flow systems. .-
Bottom of sand tank P . j
..> flow systems
Figure 31C. Increase in recharge rate decreases amount of flow downslope passing beneath the drain.
.
Figure 31 Strcarnl~nss of flow for e constant slope and vsrylng recbsige rarer
7.1750 G d l i Bumw d R.rl-mnlma
CONVERSION FACTORS-BRITISH TO METRIC UNITS OF MEASUREMENT
The f o l l o ~ ng convcrtion factors aaopled by #he 8;rea. of Rmarnation are more pb l i lhed of the American Sociew for Tenng ano Materiar IASTM Metric Practice Gu de. E 360.681 excepl that ~dd : l ' on l l f r t o r r 1.i common v used in cne Bvrea~ hwe been addd. Fvnher d8u~r imn of def n.t onr of qumt i tw i and ~ n ' u ir s 'an in
" I _ the ASTM Metric Practice Guide.
The metric units and mnvrmion factors adooted bv the ASTM are bared on the "International Svstem of Units" ldcr'gnjted 51 for Syrtcme hternatiooal d ~ n t & . f w o b, me Internatonal Committee for Weishu and Mesurer: this rystem is also r n o m as the G o r g or MKSA imeirr.k~logrm lmarl.ucona-lmperel ryrtem. This rynem ha, been adomcd of ha lntsrnationol Organ'zstio? for Standard d o n n IS0 Resommcno,cion R3:.
The metric t ~ h n i c a l unit of force is the kilogram-form; this i r the force which. whsn appl id YO a body h d & a m a s o f 1 kg, gives it an eceleration of 9.80665 mlreclrec, the standard saelerdtion of free fall toward ;he e n + center for sea level at 45 deg latitude The metric unit c f force in SI unitr is he newton (Nl: which is defined a:, . that f o m which, when applied ro a body having a mass of 1 kg. giver i t an acceleration of 1 mlredm. There unitr mun be distinguished from the (insonstant) local weight o f a body having a mas of 1 kg, that is, Uleweight of a body is that form with which a b d y is attracted to the earth and is equal to the mars of a body mul t ip l id by the accelerstian due to gravity. However. beau= it is general ~ r a ~ t i s e to use "pound" rather than the technically correct term "pound-farce." the term '%ilogam" lor derived mars unit1 has k e n used in this guide instead of "kilogram-force" i n expressing the conversion i x t o r r for forcer. The newton unit of force will find increasing "re. and ir enential in SI unitr.
Where approximate or nominal Englih units are ored m express a value or range of valuer, the converted metric unitr in ~a~entherer are also approximate or nominal. Where precise En#ish unitr are used, the converted metric unitr are expressed as equally significant valuer.
Table I ':
WANTITIES AND UNITS OF SPACE
LENGTH
. . . . . . . . . . . . . . . . . . . . . . Mil . . . . . . . . . . . . . . . . . 25.4 lexactly) Micmn
. . . . . . . . . . . . . . . . . . . Inches . . . . . . . . . . . . . . . . 25.4 (exactlyl Millimeters Inches . . . . . . . . . . ' . . . . . 2.54 Ie~actlvl ' . . . . . . . . . . . . . . . . . . Centimet~rs Feet . . . . . . . . . . . . . . . . : 30.48 lexastlyl . . . . . . . . . . . . . . . . . . Centimeters
. . . . . . . . . . . . . . . . . . . Feet . . . . . . . . . . . . . . . . 0.3048 lexactlyl. Meters . . . . . . . . . . . . . Feet . . . . . . . . . . . . . . . . O.WO3048 lexactiylf .' Kilometers
Yards . . . . . . . . . . . . . . . . C.9144 lexactlyl . . . . . . . . . . . . . . . . . . . . Meters Miier lnaturel . . . . . . . . . . 1.609.344 (exactlyl' . . . . . . . . . . . . . . . . . . . . Mewm Mil- . . . . . . . . . . . . . . . . i: 1.609344 (e~actlyJ . . . . . . . . . . . . . . . Kilometen
, ,
. . . . . Square lneher Square feet . . . . . . Square feet . . . . . .
. . . . . Square yardr Acnr . . . . . . . . . . Acres . . . . . . . . . . Acre6 . . . . . . . . . . Square miles . . . . .
. . Squarecentimeters
. . Square centimeters
. . . . . Square meterr
. . . . . Square meters
. . . :. . . . Hmtares
. . . . . Squaremeterr
. . Square kilometers
. . Souare kilometerr
VOLUME
. . . . . . . . . . . . . . . . . . . Cubic inches . . . . . . . . . . . . . 16.3871 C h i c centimeters . . . . . . . . . . . . . . . . . . . Cubicfeet . . . . . . . . . . . . . . . 0.0283168 : Cubic meters . . . . . . . . . . . . . . . . . . . . Cubic yards . . . . . . . . . . . . I 0,754555 Cubic meterr -
. . . . . Cubic centimeters . . . . . . . . . Milliliter$ . . . . . Cubicdmimeterr
CAPACITY
Fluid ounmr IUS.1 . . . . . . . 29.5737 . . . . . . . . . . . . . . Fluid ounces IU.S.1 . . . . . . . 29.5729 . . . . . . . . . . . . . . . Liquid p ins U S . ) . . . . . . . . . . 0.473179 . . . . . . . . . . . . .
. . . . . . . . Liquid pints IU.S.1 0.473166 . . . . . . . . . . . . . Quans 1U.S.) . . . . . . . . . . . '946.358 . . . . . . . . . . . . . . . Ouare 1U.S.) . . . . . . . . . . . .0.946331 . . . . . . . . . . . . . Gallons 1U.S.) . . . . . . . . . . . '3.785.43 . . . . . . . . . . . . . . . . Gallons IU.S.1 . . . . . . . . . . . . 3.78543 . . . . . . . . . . . . . .
. . . . . . . . . . . . . . Gallons lU.S.1 . . . . . . . . . . . 3.78533 . . . . . . . . . . . . GallonrIU.S.1 . . . . . . . . . . . . *0.00378543 . . . . . . . . . . . . . . Gallonr 1U.K.l . . . . . . . ; . . 4.54609
. . . . . . . . . . . . . Gallons 1U.K.) . . . . . . . . . . 4.54598 Cubic fret . . . . . . . . . . . . . 28.3180 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic yardr '764.55 Literr . . . . . . . . . . . . Acrefeet . . . . . . . . . . . . . . . . . . . . . . . . '1,2355 Cubic meters . . . . . . . . . . . . . Acrefeet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . '1,233,500 Literr . . . . . . . . . . . . .
. . . . . Cubicdecimeters . . . . . . . . . . . . Li ten . . . . . . . . . . . . Liters
- QUANTITIES AND UNITS OF MECHANICS Uulttply 8,' -. To oblrln -. Mulllply BY
- WORK AND ENERGY:.
--- MCSS .. Br i r i h thermal vniis ln tu l . . . . Y.252 . . . . . . . . . . . . . . . . . . . . . . Kil~oramcalorlsr Grain. 1117 .0~ lb 6479bal I~xacUy l . . . . . . . . . . . . . . . . . . . Mil l igram
31.1035 . . . . . . . . . . . . . . . . . . . . . . . . . Grams 28.3495 . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grams
0.45355237 lexacflyl . . . . . . . . . . . . . . . . . Kilogramr 907.185 . . . . . . . . . . . . . . . . . . . . . . Kmgrzmr
0.907195 . . . . . . . . . . . . . . . . . . . . . . . . . . . Me!ric fmr, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1918.05 Kilogram
B r i t i h thermal un ia 1 8 ~ 1 . . . . 1.055.06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . JOUI~S
' B f u pet pound . . . . . . . . . . . . 2.326 lerretlvl : . . . . . . . . . . . . . . . . . . . . . . Joules per gram FWI-pounds . . . . . . . . . . . . . '1.35582. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b u l e r
Hmrreywcr . . . . . . . . . : . 745.700 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Watts Bru per tiour . . . . . . . . . . . . 0.293071 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wrm
. . . . . . F eolpncindr per r~cand 1.35582 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W m r -.
P o u n d s ~ e r m ~ m i m h . . . . . . . m70307 . . . . . . . . . . . . . . . . ~ i l o g i a n r per quaiecrntirmtcr HEAT TRANSFER Paul~oroeialusre inch . . . . . . Om5476 . . . r.8 . . . . . . . . . . Nowlonrprr muar~rontimeter ,,2 dcpree Paundr p e r w a r e foci . . . . . . . +.RE243 . . . . . . . . . . . . . . . . . . . . ~i logrumr perrguare . . . . . . . thermal mnduclivilvl 1.442 . . . . . . . . . . . . . . . . . . . . . Milli+valolrmrlearcc C Pounds W ~ Y I Y ~ ~ O loo< . . . . . . 47.8803 Nmlon lpc r g " a E B,, in.1hrf,2dLgrpe iI, . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . MASSIVDLUME IUENSITYJ
Thermal cosdunivilyl 0,1240 Kgcsl l l i rmdegre~ C . tliu h lh r H2 a K e e F . . . . . . . . '1.4880 . . . . . . . . . . . . . . . . . . . . . Ka c,ll mlhr m2 dcorcc C
BENDING MOMENT OR TORQUE
- . Btulhr H2dcgr& F iC.
thermal conductmeel . . . . . . . 055n . . . . . . . . . . . . . . . . . . . . . . . Milliwattdrm2 d w ~ e c 'Btu lh i h2degrm F IC.
~lsrmul-andurrancel . . . . . . . 4.882 . . . . . . . . . . . . . . . . . . . . . . . . K ~ ~ ~ I I ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ c Dearc<F hr(i7i8tu IR.
. . . . . . . thcrmsi rarinance) 1.761 . . . . . . . . . . . . . . . . . . . . . . . Oogrw ~ c n l ~ l m i l l i r i r l f . . B W l b degree F Ir. Iko l capacity1 4 l 8 6 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J lgdagrsC
. . . . . . . . . . . siul l lr degree F I . . . . . . . . . . . . . . . . . . . . . . . . . . Callgram dagaeC . . . . ~ k ~ f i r i t he rm i di l lvi ivi fyl 0.2581 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cm2/rrc . . . . ~ f ~ h r ith?rmal d i f fur iv i~y l '0.W290 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : ~ ~ l h r - .. -
WATER VAPOR TRANSMISSION - -- - - - - - -. -- -- - Grl,nr,hr 1 J i,""h., "l"",, .- ~ ~~
. . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . Inch-wundr . . . . . . . . . . . 0.011521 . . . . . . c . . . . . . . . . . . . . . . . . M e ! e r . k i ! ~ ~ ~ ~ ~ ~ tranrmirrionl 16.7 . ! Grams124 hr m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . ~ ~ ~ h . ~ ~ ~ ~ d ~ 1.12985 106 .i . j, Psrmr ipcrmeanrel :. n.659 ~ c t , i ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fmr.pDundr 0,138255 ::, M~ ilngran,s P"m-inch=sj,wmeailitrl 1.67 Melric peim-conlimelm - -- - .- F o v l ~ o u n d s . . . . . . . . . . . " I35582 x lo7 . . . . . . . . . . . . . . . . . . . . . . Cmtimeter-dynes ii
Fmwound .~e r inch . . . . . . . . 5.4431 . . . . . . . . . . . . . . C e n t i m e f a r k i l o g r a m 3 P ~ ~ ~ ~ ~ t ! m e ~ ~ r ~ Uu8lre-lncher . . . . . . . . . . . 72.W8 . . . . . . . . . . . . . . . . . . . . . . . . . ~ , ~ m . ~ ~ ~ ~ , ~ ~ t ~ ~ , -- -- VELOCITY
Festoer =arm . . . . 30.48 lclactlyl . . . . . . . . . . . . . . . . . . Centimeten per rerond F e u per wsond . . . . . . . . . . . 0.3048 leracllyl' . . . . . . , . . . . . . . . . . . Meters per %and .. ". F s t per year . . . . . . . . . . . . . l .0.965873 x . . . . . . . . . . . . Centimelerrper PSO,,~
M i l cs~c r haw . . . . . . . . . . . . 1.609344 leracllyl . . . . . . . . \(. . . . . . . . Kilan#eIws p r h o u r Milsr per hour . . . . . : . . . . . . 0.447M lczarl lvl . . . . . . . . . ::; . . . . . . . . Meterr per wcond
' ACCELERATION'
!I . . . . . . . . . . . F m t p ~ r wcond2 '33048 . . . . . . . . . . . . . . . . . . . . . . . . Meterr p r r c rnnd2 - FLOW
Cubic f e t p e r s ~ o n d Ismnno-lcefl . . . . . . . . . . . . '0.028317 . . . . . . . . . . . . . . . . . . . . . Cubic meterroer r rmnd
Cubic lrrl per minute . . . . . . . . 0.4719 . . . ' ! . . . . . . . . . . . . . . . . . . Lilsrsper rpmnd Gallons Ws.1 w r <:ut~ . . . . . . 0083W . . . . . . . . . . . . . . . . . . . . . . . . . itemp per w a n d
Pcrnds . . . . . . . . . . . '0.453592 . . . . . . . . . : . . . . . . . . . . . . . . . . . . . ~ i lapremr Pounds . . . . . . . . . . . . . . '4.482 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Navtonl Pounds . . . . . . . . . . . . . U . 4 4 8 2 ~ l o 5 . . . . . . . . . . . . . . . . . . . . . . . . . . ~ y n e r
.-, --
OTHER QUANTITIES AND UNITS
M ~ l l l p l " --- BY To ohtam
Lumens par q ~ s r e foot (foot-candles1 Ohme in~ la rm i l r w r l o o l ..:.... Mi1liC""er 0.. cubic fool . . . . . . . Milliampr per mu.re loot . . . . . . . Gallons per square yard . . . . . . . . Poundsper inch . . ! . . . . . . . . . .
. . . : . . . . K l I ~ ~ ~ I t ~ p ~ ~ r n i l l l n ~ e t e r Lumen, per rquare mc,., . . . . . . . . . .
. . . L i l i r p e r q u o r o meter . . . . . . . . .
. . . . . . . . . . K l l ~ g r m n w cenlimeter
., . .
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Sal!JoAd alqal laleM pue rafimps!p up,(] 'uo!le6!1>! alelnu!r 01 23epnr pues aql uo ale, hpealr e le pa!ldde SeM (afileqm) AalsM'wonq quel aql anqe y z qehlalu! q3 le quel puer aql u! p a q d alaM a!!% p~nllno!&e alelnw!r o l r y e l a p m WM Suol q og pue 'daap 14 jy1-z 'ap!M 14 z (quai MOIJ) quel puer 6u!q1 v 'puel Su!dolr w m j afieu!e,p hpnlr a apew S ~ M uo!~efi!~ranu! uv
'pazhpue alaM 3url puer aqa u! luawamu LaleM pue 'sa(!pld qqel lalsM 'la6~etpqp u!elp uodn ale1 a f i~eqm pue adols $0 w a y 3 .ru!elp uaamaq 6u!lln330 pla!) lepualod aw ~ U I M O L ~ ~ w w f i q p pue 'rau!lqeanr aAp aqi 40 rqde~f io loq 'sal!pid a w l meM' aql l o r l q d 'raBqor!p u!elp aql &c talqel Sapnpu! llodal au1 '%01 01 0 uaawaq sadols lo$ auer aql a>aM wolioq yusl aqx o l lelna!puadnd pamreaw ral!}oId alqel raleM 'Pale wn!lq!l!nba aql u! pue elel afileqm ua@ e m j 'fiu!oedr u!mp l o 'ale1 afileqsal 'adols 40 ssalple6a~ 'sisal 11s fiu!mp paunuo uo!j!puoo s ! ~ ~ ' s u ! B A ~ Su!lsmda o m uaamlsq pagdde MleM $0 lunowe aq1 palenba saSreq3s!p u!elp aql amqm quel pues 6u!dolr aql $0 qlfiual,a~pp!w aql u! paunom ean wn!,q!l!nba w 'su!elp uaawaq pp!) le!lualod sql u!slqo 01 ap!r quel aql uo w ! o d l e apeu aim rluawa,nseaw alnssald 'pues aql u! luawanoru JalPM JO rup!a>al!p fiu!hro~s Pau!elqo rau!pyealra pun yuel aql ow! ahp 6u!anpo~lu! apew alaM n ra l mod '%OL 01 0 w o q sadols quel pues pue'r6upedr u!elp 11-21 pUe .g 'sale1 afileqoa lualajgp q l ! ~ r l rs l w JOJ palnsealu alaM ral!$o~d alqq :aim pue safileqos!p u !eq 'UO!IP~!JI! aelnlu!~ 01 aoagns pues aql uo ale, hpwe e le pajldde seM (afilaqm) meM.wol loq yuel aqr anoqe I) 2 slemalu! 11-g le qua1 puas aql u! paoeld elam sl!l lelnlln3!16e alelnw!s 01 ru !eq 'pam SeM 6uol 14 09 pue 'daap I) 211-2 'ap!M 1) z (yuel MOIJ) yuel pues fiu!ll!l v 'pus! 6u!dolr u o q afieu!e~p hpnls 01 ape", rsM uo!lefi!~sanu! u v
LABORATORY TESTSTO STUDY DRAINAGE FROM SLOPING LAND LABORATORY TESTSTO STUDY DRAINAGE FROM SLOPING LAND Bur Reclam Rep RECERC7Z-l. Div Gen Rer, Jan 1972, Bureau of Reclamation, Denvet. 61 p, Bur Reclam Rep REC-ERC-72-4. Dlv Gen Rer, Jan 1972. Bureau of Reclamation, Denver, 61 p, 34 flg, 4 tab. 8 photo. 2 ref 34flg. 4 tab, 8 photo. 2 ref
DESCRIPTORS-/ groundwater flow1 subsurface drains1 water table1 steady flow1 horizontal drainrl *rubrurface drainage1 .laboratory tertrl 'tert rerultrl plartic tubing1 rloperl water recircdationl *groundwater movement1 'porous materialrl water measurement1 infiitration
I ratel permeability tertrleffectr
DESCRIPTORS-/ groundwater flow1 subsurface drains/ water tablel steady flow1 horizontal drains1 'subsurface drainagel 'laboratory tests1 *test results1 plestic tubing! slopes1 water recirculatianl 'groundwater movement1 'porour materialrl water mearurementl illfiltration rate1 permeability tertrl effects
Zeigler, E R Ze~gler. E R LABORATORY TESTSTO STUDY DRAINAGE FROM SLOPING LAND LABORATORY TESTSTO STUDY DRAINAGE FROM SLOPING LAND Bur Reclam Rep REC-ERC-72.4, Div Gen Rer. Jan 1972. Bureau of Reclamation. Denver, 61 P. Bur Reclam Rep RECERC-72-4. Div Gen Rer. Jan 1972, Bureau of Reclamation. Denver. 61 p. 34 fig. 4 tab. 8 photo, 2 ref 34 fig, 4 tab. B photo, 2 ref
DESCRIPTORS-/ groundwater flow1 rubrurface drainsl water tablel steady flaw/ horizontal
i drains1 'rubrurface drainage1 'laboratory tertr l 'tert results/ plastic tubing/ slopes/water recirculation1 'groundwater movement1 'porous materials1 water mearuiementl infiltiatian rate/ permeability tests1 effects
!
DESCRIPTORS-/ groundwater flow1 rubrurface drains1 water table1 steady flow1 horizontal drains1 'subsurface drainage1 'laboratory tertr l 'ten rerultrl plartic tubing1 slaperl water recircularion1 'groundwater movement1 'porour matcrialrl water measurement1 infiltration rate1 permeability tests1 effects